*multiplicity.*In situating their respective work according to this shared commitment to multiplicity, a second commitment-in-common to multiplicity articulated with mathematical concepts and tools comes into view. Deleuze and Guattari deploy Bernhard Riemann ’s innovations in non-Euclidean geometry , and a particular interpretation of differential calculus . In Badiou’s case, it is his well-documented use of principles at the foundation of set theory and its revisions in the late nineteenth and twentieth century, particularly Cantor’s inconsistent and consistent multiples, the Zermelo–Fraenkel axiom system, and insights from Bourbaki .

*Deleuze: la clameur de l’être*, a text published in English as

*Deleuze: The Clamor of Being*(2000; hereafter

*Clamor*). The conversation, when it turns to questions of multiplicity and ontology , reveals objections and demands concerning the structure of multiplicity, the way certain of the mathematical and conceptual tools are deployed to organize being qua being, and the procedures these chosen structures prescribe for handling any one in relation to this multiplicity. The prospects for approaching this as a conversation are aided considerably by my temporal distance from the original set of exchanges. I am, as it will become clear below, one in a lineage of thinkers that have taken up the Deleuze–Badiou knot; my contribution emphasizes the unique strategies each thinker takes when approaching the so-called “being question,” and identifies the places where these differences give way to continuous commitments, namely the demand to arrive at and maintain the multiple using some form of subtractive procedure.

*Pequod*, in which Ahab enjoins young Starbuck to “come closer … thou requirest a little lower layer.” Ahab’s comment is something of an existential injunction and, for the purposes of this project, a useful procedural reminder. As a reader of the Deleuze–Badiou corpus and one attentive to their exchanges, it is significant to consider how, precisely, Deleuze and Badiou each bring their reader to the site of multiplicity in their ontological projects, how they identify multiplicity with a fundamental aspect of being; and how, in Melvillian parlance, they, respectively, admonish their readers to seek this lower layer underwriting that which appears, a lower layer linked to and fundamental to its operation.

## Orientations

*Being and Event*, which appears in shorthand as “mathematics = ontology ” (

*BE*xiii). The Nirenbergs challenge the contention that mathematical ontology , in general, and especially that proposed by Badiou , produces the sorts of things it claims to; for example, they insist that Badiou’s particular—and by their lights,

*peculiar*—use of set theory is selective in its deployment and its consequences. The Nirenbergs claim that set theory cannot be used to justify the philosophical or political conjectures Badiou draws in

*Being and Event*, and further that the identity of ontology and mathematics Badiou proposes precludes the possibility for “pathic” elements, namely human thought, to emerge from the mathematical system (Nirenberg and Nirenberg 2011, 606–612). This approach, they insist, “will entail such a drastic loss of life and experience that the result can never amount to an ontology in any humanly meaningful sense” (Nirenberg and Nirenberg 2011, 586). The Nirenbergs operate according to the view that ontology is an inquiry into being and questions related to existence as these pertain to humans; they laud the resources of phenomenology , for example, insofar as this method derives conclusions of what it is “to be” from lived experience. By emptying ontology of these resources—a traditionally human center and the lived experience that accrues to it—the Nirenbergs see Badiou’s use of set theory to be so reckless as to endanger an entire tradition of thought.

*Critical Inquiry*, the discussion unfolds with accusations that one camp has fundamentally misunderstood the other. Bartlett and Clemens insist that the Nirenbergs have not read Badiou’s oeuvre carefully; the Nirenbergs fail to understand that ontology as mathematics, for Badiou,

*really*functions as a “figure of philosophical fiction” (Bartlett and Clemens 2012, 368). Badiou , explaining that Bartlett and Clemens respond to the Nirenbergs with “polite irony,” calls the criticism raised by the Nirenbergs “stupid” (2012, 363–364). While significant points both in defense and critique of Badiou’s program are raised in these pages, the interlocutors seem largely to talk past one another; the insights are, unfortunately, lost in the polemical nature of the interchange.

*Being and Event*situates “mathematics is ontology ” as the

*consequent*of a preliminary claim: “Insofar as being, qua being, is nothing other than pure multiplicity , it is legitimate to say that ontology , the science of being qua being, is nothing other than mathematics itself” (

*BE*xiii). Badiou spends the first five meditations of

*Being and Event*arguing for the

*antecedent*claim that being qua being is multiplicity. This claim is not mentioned in the Nirenberg–Bartlett –Clemens–Badiou

*contretemps*; it is neither a matter of common sense nor established fact, and it led me to ask a further question following this debate: What

*does*Badiou mean when he claims being qua being is pure multiplicity?

### Badiou’s Multiplicities

*One*or

*many*. Badiou’s opening salvo in Meditation One of

*Being and Event*is to show this debate as having stagnated:

For if being is one, then one must posit that what is not one, the multiple, is not. But this is unacceptable for thought, because what is presented is multiple and one cannot see how there could be an access to being outside all presentation … On the other hand, if presentation is, then the multiple necessarily is. It follows that being is no longer reciprocal with one and thus it is no longer necessary to consider as one what presents itself, inasmuch as it is. This conclusion is equally unacceptable to thought because presentation is only this multiple inasmuch as what it presents can be counted as one; and so on. (BE23)

*one*thing. These positions are so entrenched, Badiou claims, that he must enact a

*decision*that breaks the impasse and can restart ontological questioning anew. This decision consists in the claim that “the one

*is not*” (

*BE*23), which means by implication that the multiple is Badiou’s preferred solution to the question of being, at least as he has presented the available options.

*not*material and does

*not*consist in the ‘bodies’ associated with these older positions. Rather, Badiou ’s multiple is articulated in three ways, each according to mathematical innovations: The first and second—

*inconsistent*and

*consistent*multiplicities—are derived from work by Georg Cantor . The third—

*generic*multiplicity —comes from Paul Cohen’s more contemporary work.

*first,*

*second, third*). To avoid the contradiction that arises from the presence of an ordinal not counted in the set of all ordinals, Cantor posits a consistent multiple that is closed and organized according to the typical rules of the set...